Magic Online prize schedules

[phlip]

So, this is branching from a discussion here about the Limited Resources Managing Your Bankroll episode, which talks about maximising your payout (or minimising your costs) for drafting on Magic Online. In particular, which prize schedule (Swiss, 4-3-2-2 or 8-4) you should play. This discussion spiralled out from there, and I'm branching this off to not clutter up that thread with my mathy rambling.

Their math is flawed and the basic economics they based it on is flawed. It is true that wizards pays 12 packs for 8-4 or swiss, and 11 packs for 4-3-2-2, so for ALL players the pay out is less.

It's not based on that fact, though that fact is related to what actually comes out in the calculations. But even if it was a 5-3-2-2, and they were all even, the window for which the 5-3-2-2 would be the right choice would still be narrow. In the simplification where you have the same %-win chance in Swiss, 5-3-2-2 and 8-4, there's still no point where 5-3-2-2 is the optimal choice... it's just that at exactly 50%, now all the options are the same, rather than 4-3-2-2 still being noticeably less. The only window where 5-3-2-2 becomes better is from the adjustments from having a better chance of winning in one queue compared to another. Which is narrow.

Where this "total amount of packs given out" can be relevant is for the case where your percentage to win is exactly 50%... in that case it doesn't actually matter what the payout schedule is, because once you figure out how much you pay out to the 8 records (WWW, WWL, WLW, WLL, etc), you're equally likely to be any of those 8. So your expected payout is just "number of packs given out / 8"... which is 1.5 for 8-4 and Swiss, but 1.375 for 4-3-2-2... so if you're at the level where you're 50% to win a round, then your EV with Swiss and 8-4 (and 5-3-2-2) are the same, and both better than 4-3-2-2.

If you play a 8-4 if you win 3 games you get 8 packs, if you win 2 games you get 4 packs, 6 people get 0 you have a 25% chance of any packs.

But this is one of the "psychological effects" I was alluding to before. 4-3-2-2 feels better than 8-4 because you have a better chance of walking away with anything, even if it's small. And 4-3-2-2 feels better than Swiss because the first round is worth two packs, and each subsequent round is worth one, which is more than the individual rounds in Swiss are worth.

However, in an 8-4, you have a lower chance of winning packs, but when you do, your payout is higher. And, if your percentage-to-win chance is high enough, over the long term you'll win more with an 8-4 than with a 4-3-2-2... sure, you'll pay out less often, which might feel worse, but when you do pay out you'll win by more than enough to cover the difference.

On the other hand, if your percentage-to-win chance is lower than that threshold, then in a 4-3-2-2 you're reasonably likely to lose the first round... and in that case, you're out, no gain, while in a Swiss you'd get to keep playing, and still have a chance of winning something. Only one of the eight players in a Swiss walks away empty-handed. And, in this case, these additional chances outweigh the fact that a 4-3-2-2's payouts are higher. So you will bleed out slower, as you put it.

you play 10 games you will one, take second twice, and take 3/4th five times and scrub out twice cause you just dont get any cards or you play that amazing 4 pack rat draft first game.

in 8-4 you win 16 packs paying in 30 packs you are down 14 packs.

in 4-3-2-2 you win 20 packs with the same 30 pack investment and are down 10.

Those numbers are crazy... you're saying you're 80% chance to win the first round (only 2/10 to scrub out first round), but then only 37% chance to win the second round, and 33% chance to win the finals? This is single-elim, remember. If you're assuming you have a 50% chance of winning a round (which you seem to be assuming a lot), then it should be 1-and-a-bit wins, 1-and-a-bit seconds, 2-and-a-half 3/4ths, 5 scrub-outs. Your weird massive spike at the 3/4th place naturally favours the 4-3-2-2 payout, since it pays out at that level but 8-4 doesn't.

That puts you at 15 packs won for 8-4, 13.75 packs won for 4-3-2-2.

For someone with a lower win rate, say, 1/3, they'd expect from 10 tournaments, to have 0.37 wins, 0.74 seconds, 2.22 3/4ths and 6.66 scrub-outs. That puts them at just under 6 packs won from 8-4s, but just over 8 packs won from 4-3-2-2s. However, in a Swiss they would have 0.37 3-0's, 2.22 2-1's, 4.44 1-2's and 2.96 0-3's... which puts them at 10 packs won (as expected... with a win rate of 1/3 they should expect 1 pack won per 3-round draft), making Swiss better than either of the single-elim options.

50% is the magic crossover point where 8-4 becomes better than Swiss... at no point is 4-3-2-2 (or even, as mentioned above, 5-3-2-2) the best option. And, as I mentioned before, all the 12-pack-payout curves cross through the same point at 50%, while 4-3-2-2 stays a ways below it.

[Lord Hosk]

The reason that I put a big hit on winning the first round is I am talking about the 50% player. Someone who is better than worse but not in the top tear. The player who is in the top 40-50% will likely get to round two far more frequently than final or first round scrub out.

In order to make 8-4s good have to be in the top 20% of players. You have to get to the final round more than 50% of the time.

So if you are in the 50-80 range I would contend that you get more drafts out of a 4-3-2-2, But in the lower 50 you are going to get the most drafts out of swiss.

I would say that only the top 5% have a chance at "going infinite" so the real goal has to be how slowly do you lose your bank roll and for a slightly above average player that isnt 8-4, but the top 20% players want as many none-top 20% players as they can get in the 8-4s or they dont win.

[phlip]

I'm still thoroughly confused how you think a player "in the top 40-50%" is supposed to win the first round of a 4-3-2-2 80% of the time... Are these numbers you've got from somewhere, or just guesswork?

Also, I agree going infinite isn't the aim here. But even for someone who isn't hitting that magic level, I still contend that either 8-4 or Swiss are going to be better at stemming the bleeding than 4-3-2-2 is.

[Lord Hosk]

a player in the top 40-50% will win the first round of a 4-3-2-2 roughly 80% of the time based on the that he or she is better than 50-60% of mtgo players. 4-3-2-2s are the most common draft format based on the quick sampling I just did, out of 50 drafts running on MTGO there were 29 4-3-2-2s so 58% of drafts. when you factor in that the best players are typically running 8-4s and the new worse players are running swiss you get a general idea that the population playing 4-3-2-2s will be something in the range of the middle lets say the middle 75%. although some people who think they are better than they are run in the 8-4 and some people who are casual will just run swiss but without hard data from wizards and a month to crunch the data you have to start with some presumptions.

if the middle 75% are in your que and you are better than 50-60% of the people as a whole there will be one to three players on par or better than you which means that there are 4-6 worse than you you have over a 50% chance of playing against a inferior opponent in the first round you have roughly a 25% chance of facing a much worse player than yourself, now the game of magic isnt a simple coin flip, or a game of pure skill but the better you are the better you build you deck and the more chance you have of winning. Anyone can have a dream curve and top deck the perfect answers to your opponents play and anyone can just flood out or get mana screwed, but over the long game which is what we are talking about here, skill trumps luck.

The reason that I am opposed to the 8-4 argument is what Marshal himself said and he may have meant it, he may have subconsciously dropped it, or he may have been intentionally misleading, from everything I have heard or read about the guy I highly doubt it was intentionally misleading but I dont know him so its possible. He said "Not even the good poker players want their table statistics to be put out there because if people see how much money they lose to the big players in stark black and white they wont play anymore." People keep dumping money to high caliber poker players because they win big occasionally and it feels good to get the big win. If lower caliber players didn't play in the 8-4s relying on the rush they get from winning 8 packs once in awhile the top 20% wouldn't be able to make money off them. I really dont care what anyone plays, I dont play enough to make any kind of run, this is all purely academic for me.

The only solid data I can go off of is Kenjis streams because he does it SO much, if you look at the last round of his 8-4s the same opponents pop up frequently this is because they are those top 20% of players. Something he often says when he loses in the first or second round and even when its a very close win is "oh I recognize this guy" When he recognizes his opponent its because they are a better player while there are some people out there, we have all met them, who are willing to throw thousands of dollars away on the game most people who play a lot do so because they win enough to keep rolling on their initial investment and that is on the backs of the less skilled players who jump into the 8-4s hoping for the rush of a win.

You have repeatedly said that people play 4-3-2-2s because it feels better to win a little all the time, I would contend that people play 8-4s because it feels better to get to the last round or even win once in awhile. It feels good to put on your big boy pants and get the rush of a win.

You discount the idea that the economics of Wizards Vrs players is a big part of the argument against 4-3-2-2s but is pretty much all John talked about. He kept going back to the fact that the pay out is lower by 1 pack and saying things like "well if you just want to throw away one potential pack you can but that hurts you because thats throwing away a draft for every three you enter" It was his primary argument against the 4-3-2-2s he barely talked about the chart other than to say "you can see on the chart its such a slim margin"